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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 3, Pages 456–475 (Mi tvp1554)  

This article is cited in 9 scientific papers (total in 9 papers)

Cramer large deviations when the extreme conjugate distribution is heavy-tailed

A. V. Nagaev

Nikolaus Copernicus University

Abstract: The classical large deviations problem is considered under the assumption that the unilateral Cramer condition holds on a bounded interval. We assume that the extreme conjugate distribution is from the domain of attraction of a stable law. A limit is established up to which the asymptotic Cramer–Petrov representation is valid.

Keywords: conjugate distribution, slowly varying function, monotone $\varepsilon$-approximation.

DOI: https://doi.org/10.4213/tvp1554

Full text: PDF file (747 kB)

English version:
Theory of Probability and its Applications, 1999, 43:3, 405–421

Bibliographic databases:

Received: 05.11.1996

Citation: A. V. Nagaev, “Cramer large deviations when the extreme conjugate distribution is heavy-tailed”, Teor. Veroyatnost. i Primenen., 43:3 (1998), 456–475; Theory Probab. Appl., 43:3 (1999), 405–421

Citation in format AMSBIB
\by A.~V.~Nagaev
\paper Cramer large deviations when the extreme conjugate distribution is heavy-tailed
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 3
\pages 456--475
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 3
\pages 405--421

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    This publication is cited in the following articles:
    1. L. V. Rozovskii, “Large deviation probabilities for some classes of distributions, satisfying the Cramer condition”, J. Math. Sci. (N. Y.), 128:1 (2005), 2585–2600  mathnet  crossref  mathscinet  zmath
    2. A. Yu. Zaigraev, A. V. Nagaev, “Abelian theorems, limit properties of conjugate distributions, and large deviations for sums of independent random vectors”, Theory Probab. Appl., 48:4 (2004), 664–680  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. A. Vatutin, “Limit theorem for an intermediate subcritical branching process in a random environment”, Theory Probab. Appl., 48:3 (2004), 481–492  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. A. Borovkov, K. A. Borovkov, “On probabilities of large deviations for random walks. II. Regular exponentially decaying distributions”, Theory Probab. Appl., 49:3 (2005), 189–206  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. A. Borovkov, A. A. Mogul'skii, “On large and superlarge deviations for sums of independent random vectors under the Cramer condition. I”, Theory Probab. Appl., 51:2 (2007), 227–255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Jorgensen B., Martinez J.R., Vinogradov V., “Domains of attraction to Tweedie distributions”, Lithuanian Mathematical Journal, 49:4 (2009), 399–425  crossref  mathscinet  zmath  isi  scopus
    7. Touchette H., “The large deviation approach to statistical mechanics”, Physics Reports–Review Section of Physics Letters, 478:1–3 (2009), 1–69  crossref  mathscinet  isi  scopus
    8. L. V. Rozovskii, “Superlarge deviation probabilities for sums of independent random variables with exponential decreasing distributions. II”, Theory Probab. Appl., 59:1 (2015), 168–177  mathnet  crossref  crossref  mathscinet  isi  elib
    9. A. A. Borovkov, “Moderately large deviation principles for trajectories of compound renewal processes”, Theory Probab. Appl., 64:2 (2019), 324–333  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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